Temperature Profiles of Accretion Disks in Luminous Active Galactic Nuclei derived from Ultraviolet Spectroscopic Variability

The characteristic timescale ($\tau$) of continuum variability of the accretion disk in active galactic nuclei (AGNs) is known to be related to the thermal timescale, which is predicted to scale with AGN luminosity ($L$) and restframe wavelength (${\lambda }_{\mathrm{R}\mathrm{F}}$) as $t_{\mathrm{t}\mathrm{h}}\propto L^{0.5}{\lambda }_{\mathrm{R}\mathrm{F}}^2$ in the standard disk model. Using multi-epoch spectroscopic data from the Sloan Digital Sky Survey Reverberation Mapping project, we construct ultraviolet ensemble structure functions of luminous AGNs as a function of their luminosity and wavelength. Assuming that AGNs exhibit a single universal structure function when $\mathrm{\Delta }t$ is normalized by $\tau$, wherein $\tau \propto L^a{\lambda }_{\mathrm{R}\mathrm{F}}^b$, we find $a=0.50\pm 0.03$ and $b=1.42\pm 0.09$. While the value of $a$ aligns with the prediction from the standard disk model, $b$ is significantly smaller than expected, suggesting that the radial temperature (color) profile of the accretion disk is significantly steeper (shallower) than the standard disk model. Notably, this discrepancy with theory has been observed in previous studies based on spectroscopic reverberation mapping and gravitational microlensing. Although no current model of accretion disks fully matches our results, our findings provide valuable constraints for testing future physical models.